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Proof step 38 from proof path-dups (previous step)

(r ' + x1)[m] = (r ' + x1)[n], n < m, path(r ' + x1, H), m ≤ # x1, n < # x1 ⊦ n = 0, m = n, x1 = [], reachable-n(H, n, r, (r ' + x1)[n]), path(firstn(n + 1, r ' + x1), H) ∧ hd firstn(n + 1, r ' + x1) = r ∧ firstn(n + 1, r ' + x1) .last = ((hd firstn(n + 1, r ' + x1)) ' + x1)[n] ∧ # firstn(n + 1, r ' + x1) = n + 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 37:
(r ' + x1)[m] = (r ' + x1)[n], n < m, path(r ' + x1, H), m ≤ # x1, n < # x1 ⊦ n = 0, m = n, x1 = [], reachable-n(H, n, r, (r ' + x1)[n]), path(r ' + firstn(n, x1), H) ∧ (r ' + firstn(n, x1)) .last = (r ' + x1)[n]

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + n = m + n0 ↔ n = n0], [CSIMPSEQ : ⊦ # firstn(n, x0) = n], [CSIMPSEQ : ⊦ # r ' = 0 +1], [CSIMPSEQ : ⊦ # (x0 + x1) = # x0 + # x1], [CSIMPSEQ : ⊦ hd (r ' + x0) = r], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ (x0 + x1) + x2 = x0 + x1 + x2], [CSIMPSEQ : ⊦ r + x0 = r ' + x0], [CSIMPSEQ : ⊦ firstn(n + 1, r ' + x0) = r + firstn(n, x0)])]]